XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2015 $ 134 $ 3 2016 150 3 2017 125 3 2018 130 3 An investor buys five shares of XYZ at the beginning of 2015, buys another two shares at the beginning of 2016, sells one share at the beginning of 2017, and sells all six remaining shares at the beginning of 2018. a. What are the arithmetic and geometric average time-weighted rates of return for the investor

a. We have:

Arithmetic mean = 2.62%

Geometric mean = 1.82%

b. From the attached excel file, the total cash flow for each year are as follows:

January 1, 2015 Total Cash Flow = -$650

January 1, 2016 Total Cash Flow = -$273

January 1, 2017 Total Cash Flow = $141

January 1, 2018 Total Cash Flow = $768

Explanation:

Note: The requirement of this question is not complete. The complete requirement is therefore given before answering the question as follows:

a. What are the arithmetic and geometric average time-weighted rates of return for the investor.

b. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018.

The explanation of the answer is now given as follows:

The following sorted table is given in the question:

Year          Beginning-of-Year Price           Dividend Paid at Year-End

2015                           $ 134                                              $ 3

2016                              150                                                 3

2017                              125                                                 3

2018                              130                                                 3

a. What are the arithmetic and geometric average time-weighted rates of return for the investor.

The arithmetic and geometric average time-weighted rates of return for the investor can be calculated as follows:

Arithmetic average return = Sum of returns/ number of years ………….. (1)

Geometric average return = n * ((1+r1)*(1+r2)*(1+r3)…(1+rn)^(1/n) - 1 .……….. (2)

Where;

n = years 1, 2, 3….

r1, r2, r3… are the returns for year 1, 2, 3….

Return for each year = ((Current year Beginning-of-Year Price – Previous year Beginning-of-Year Price) + dividend) / Previous year Beginning-of-Year Price (3)

Using equation (3), we have:

2016 Return = ((150 - 134) + 3) /134 = 0.141791044776119

2017 Return = ((125 - 150) + 3) /150 = -0.146666666666667

2018 Return = ((125 - 120) + 5) /120 = 0.0833333333333333

Using equation (1), we have:

Arithmetic mean = (2016 Return + 2017 Return + 2018 Return) / 3 = (0.1417910447761190 - 0.1466666666666670 + 0.0833333333333333) / 3 = 0.0262, or 2.62%

Using equation (2), we have:

Geometric mean = ((1 + 2016 Return) * (1 + 2017 Return) * (1 + 2018 Return))^(1/3) - 1 = ((1 + 0.141791044776119) * (1 - 0.146666666666667) * (1 + 0.0833333333333333))^(1/3) - 1 = 0.0182, or 1.82%

b. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018.

Note: See the attached excel file for the chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018.

In the attached excel file, Beginning-of-Year Price for January 1, 2015 and January 1, 2016 are negative because the purchase of stock is a cash outflow.

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